A gain-field encoding of limb position and velocity in the internal model of arm dynamics.

Hwang EJ, Donchin O, Smith MA, Shadmehr R - PLoS Biol. (2003)

Bottom Line:
The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

ABSTRACTAdaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.

pbio.0000025-g005: Predictions of the Gain-Field Encoding and Experimental Verification(A) A field where forces are linearly dependent on both limb position and velocity.(B) A field where forces are linearly dependent on limb velocity but nonlinearly dependent on limb position. Gain-field encoding predicts that the field in (B) will be harder to learn than one in (A).(C) Learning index of subjects (n = 6) for the paradigm in (A) and subjects (n = 5) for the paradigm in (B).(D) Gain-field encoding predicts hypergeneralization. The figure shows movements and its associated force field during training and test sets.(E) Performance of subjects (n = 4) for the paradigm in (D). Dark lines are errors in center movements and gray lines are errors in right movements. The shaded areas represent the SEM. Filled diamonds show the catch trials for the left movements during test set; filled squares show the catch trials for center movements.

Mentions:
Figure 5A shows the pattern of forces that was previously shown to be easily adaptable. Figure 5B shows a similar task, where the leftward and rightward forces are separated by the same distance, but instead of making movements between the left and right positions, movements are made off to the right of the field trials. The field in Figure 5A is learnable by gain-field basis elements. However, if the internal model is indeed computed with such elements, then for the field in Figure 5B we can make two predictions: (1) this pattern of forces should not be learnable because no linear function can adequately describe this nonlinear pattern of force; and (2) movements at the “right” should show aftereffects of the center movement despite the fact that no forces are ever present.

pbio.0000025-g005: Predictions of the Gain-Field Encoding and Experimental Verification(A) A field where forces are linearly dependent on both limb position and velocity.(B) A field where forces are linearly dependent on limb velocity but nonlinearly dependent on limb position. Gain-field encoding predicts that the field in (B) will be harder to learn than one in (A).(C) Learning index of subjects (n = 6) for the paradigm in (A) and subjects (n = 5) for the paradigm in (B).(D) Gain-field encoding predicts hypergeneralization. The figure shows movements and its associated force field during training and test sets.(E) Performance of subjects (n = 4) for the paradigm in (D). Dark lines are errors in center movements and gray lines are errors in right movements. The shaded areas represent the SEM. Filled diamonds show the catch trials for the left movements during test set; filled squares show the catch trials for center movements.

Mentions:
Figure 5A shows the pattern of forces that was previously shown to be easily adaptable. Figure 5B shows a similar task, where the leftward and rightward forces are separated by the same distance, but instead of making movements between the left and right positions, movements are made off to the right of the field trials. The field in Figure 5A is learnable by gain-field basis elements. However, if the internal model is indeed computed with such elements, then for the field in Figure 5B we can make two predictions: (1) this pattern of forces should not be learnable because no linear function can adequately describe this nonlinear pattern of force; and (2) movements at the “right” should show aftereffects of the center movement despite the fact that no forces are ever present.

Bottom Line:
The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

ABSTRACTAdaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.